Question

Your professor needs a $25,000, 7-year loan. To repay you, your professor will pay $2,500 at the end of of the first year, $5,000 at the end of the second year, and $7,500 at the end of the third year, plus a fixed (currently unknown) cash flow, X, at the end of each of the last four years (fourth through and including the seventh year). Considering how much you respect this professor, you decide to charge her an APR of 8 percent. Figure out the cash flows that the professor must pay in years 4 through 7.

Answer 1

CF0 = -25,000

CF1 = 2,500

CF2 = 5,000

CF3 = 7,500

25000 = 2,500/ (1.08) + 5000/ (1.08)² + 7,500/ (1.08)³ + CF4/ (1.08)⁴ + CF5/ (1.08)⁵ + CF6/ (1.08)⁶ + CF7/ (1.08)⁷

25,000 = 12,555.25 + CF4/ (1.08)⁴ + CF5/ (1.08)⁵ + CF6/ (1.08)⁶ + CF7/ (1.08)⁷

CF4/ (1.08)⁴ + CF5/ (1.08)⁵ + CF6/ (1.08)⁶ + CF7/ (1.08)⁷ = 25,000 - 12,555.25

CF * (1/ (1.08)⁴ + 1/ (1.08)⁵ + 1/ (1.08)⁶ + 1/ (1.08)⁷ ) = 12,444.75

CF * (2.63) = 12,444.75

CF = 4,733.15

Professor needs to pay 4,733.15 each year from year 4 to 7 in order to repay loan of 25,000 over 7 year period